In the
mathematical field of
combinatorics, a
bent function is a special type of
Boolean function. This means it takes several inputs and gives one output, each of which has two possible values (such as
0 and
1, or
true and
false). The name is figurative. Bent functions are so called because they are as different as possible from all
linear and
affine functions, the simplest or "straight" functions. This makes the bent functions naturally hard to approximate. Bent functions were defined and named in the 1960s by Oscar Rothaus in research not published until 1976. They have been extensively studied for their applications in
cryptography, but have also been applied to
spread spectrum,
coding theory, and
combinatorial design. The definition can be extended in several ways, leading to different classes of generalized bent functions that share many of the useful properties of the original.